变分问题

The performance function and constraint equation in calculus of variations were constructed by analyzing input and output equations of the system containing parameters to be estimated. The traditional parameter estimation problem could be transformed to that of least squares estimation.

通过分析包含待估参数的系统输入输出方程，构造变分法中的性能范函和约束方程，将传统的参数估计问题化为带约束条件的最小二乘估计问题；利用拉格朗日乘子法，分析参数估计方程，得到参数的最优估计。

Well, he conceives God in the creation of the world like a mathematician who is solving a minimum problem, or rather, in our modern phraseology, a problem in the calculus of variations .

众所周知，通过发现切线方法，函数的最大与最小值理论取得了最大进展，这归功于莱布尼茨。他认为上帝在创世中就像一个解决最小值问题--或者用我们当代的术语说，变分法问题--的数学家。

In this paper, the computation of original likelihood function is transformed into the optimal problem of its low bound through the conjugate representation of the convex function, and a additional parameter is introduced to control the smoothing degree of low bound, and so the performance of local optimal solution can be improved.

我们利用凸泛函的对偶性，将原似然函数的复杂计算问题转化为对其下界函数的优化问题，从而降低学习算法的复杂性；并通过引入一个参数来控制下界函数的光滑程度来改善局部最优解的性能；指出了传统的期望最大化算法(Expectation Maximization Algorithm)是变分学习算法的特殊情况。

It takesthe weighted average of the L2 norm of the difference of the observation and thesolution of the system and the L2 norm of the difference of conormal derivativeat the different sides of the interface for every subdomain as cost functional andthe smooth coefficients of the subproblem and the value of solution of the originalproblem at interface as identification parameters;Using the property of continu-ous functional defined on compact set,the existence of the optimal solution of theidentification problem is proved;The necessary conditions of optimality charac-terized by the system equation,the adjoit equation and the variational inequalitysimultaneously are given by introducing the conception ofdifferential andadjoit variable;An algorithm is devised and its flow graph is given.

其次，针对分片光滑动力系统的特征，结合正演过程的区域分解算法，建立了分片光滑系统的分解区域参数辨识模型，该模型以子区域上解的实测值与计算值之差的L2范数和界面两侧的通量差的L2范数的加权平均作目标泛函，各子问题的光滑系数及界面上真解的值为待辨识参量；利用紧致集上连续泛函的性质，证明了子区域上参数辨识问题最优辨识参量的存在性；引入微分的概念，借助伴随变量，给出了由系统方程，伴随方程和变分不等式共同表征的最优性必要条件；根据此必要条件设计了算法，给出了算法的程序框图。

Based on the principle of variation, boundary value problem of pressure partial differential equation was transformed into the extreme value problem of fonctionelle and finite element equation of flow model was deduced for calculating the simulation result.

根据变分原理，将压力微分方程的边值问题转化为泛函的极值问题，建立了渗流模型的有限元方程。

At the condition of high spacial frequency, the principle and methods of image blind deconvolution has been studied, and the method of regularization image blind deconvolution based total variation has been used in the restoration problem of the 1-D bar code signals. The problem of blurring and interaction of bar signals under convolution with the SPF was solved with the method.

研究了图像盲目反降晰的基本原理与方法，并将基于总变分的正则化盲目图像反降晰方法应用到我们的一维条码信号的复原问题中，很好地解决了高空间频率条件下因光学系统点扩散函数带来的信号降晰及边缘混叠问题。

In this paper, first of all, we study the set-valued vector equilibrium problems and the set-valued vector Hartman- Stampacchia variational inequality in normed linear space.

本文首先在赋范线性空间中，研究了集值向量均衡问题和集值Hartman-Stampacchia变分不等式这两个问题的弱有效解的存在性，得到了弱有效解集的连通性和紧性结果。

Viability Theory is applied to the optimal control problem for this class of hybrid dynamic time varying systems in this dissertation for the first time. And the statement about a characterization of the extended value functions as the unique lower semicontinuous solution to a Bensoussan-Lions type QVI is proved.

本文首次将生存理论应用到这一复杂系统的最优控制问题中来，得到了最优控制问题中的值函数是一类拟变分不等式唯一的下半连续解的重要结论。

The nonlinear singular boundary value problems with one-dimensional p-laplacian comes from applied mathematics and physics and is now one of the most active research field in modern analysis.

利用变分方法、锥理论和Leggett-Williams定理，我们在本文中研究了一维奇异p-Laplacian非线性边值问题正解的存在性问题，得到了一些新成果。

It has an important relation with stationary point theories, variational inequality, linear and nonlinear analysis, and some applied mathematical problems such as economic and equilibrium problems.

它与不动点理论，变分不等式问题，线性和非线性分析，以及其他领域的应用数学如经济，平衡问题等都有密切的联系。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。